The idea behind the vectors of locally aggregated descriptors (VLAD) [1]} is to compute the embeddings by means of residuals \(x_{i} - c_{k}\)  for each local image descriptor \(x_{i}\) . Finally, embedded local image descriptors of each image are accumulated by an orderless aggregation function. This characterizes the distribution
of the vectors with respect to the cluster centers. The VLAD embedding can be regarded as simiplified version of the Fisher Vectors [1]}. More precisely, given \(N\)  local image descriptors \(\lbrace x_{i} | x_{i} \in \mathbb {R}^{D}, i=1, \dots , N \rbrace \)  and a dictionary of \(K\)  cluster centers \(\lbrace c_{j} | c_{j} \in \mathbb {R}^{D}, j=1, \dots , K\rbrace \) , the VLAD embedding function is computed as follows:
\(\phi _{\text{VLAD}, k}(x_{i}) = \alpha _{k}(x_{i})(x_{i} - c_{k})\) 
\(\alpha _{k}(x_{i}) = {\left\lbrace \begin{array}{ll}1, & \text{if } k = \operatornamewithlimits{argmin}_{j=1, \dots K} \Vert x_{i}-c_{j} \Vert \\0, & \text{else}\end{array}\right.}\) 
